PS3 doesn't always startup, how to fix?

I have a PS3 Slim and lately just after I turn it on it gives three beeps and powers down.

I have found that with persistence it will eventually start up, and once it does it will run fine all day long until it's shutdown manually.

Each time I start it up has become a battle of wills to see if it will startup or I will loose patience first. Comrades, I barely won the last battle. The situation is dire. Morale is low. It seems to be taking longer with each passing day...

Is this something I can fix or is all hope lost?

The 3 beeps on start up means that the PS3 has overheated and unseated either to CPU or GPU. You can confirm this by watching for yellow lights flashing when it starts up.

This fault is commonly known as the yellow light of death. It is likely that the PS3 will eventually stop working altogether.

To solve this, you can attempt to replace the thermal paste on the the CPU & GPU and there are various guides online about how to do this.

If you are not comfortable doing that yourself then you could take it to a professional for repair but it is probably more economical to buy another one.

Either way, you need to make sure all your saves and data are backed up.